Question: Which of the following numbers is a factor of 177? ${3,4,6,10,12}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $177$ by each of our answer choices. $177 \div 3 = 59$ $177 \div 4 = 44\text{ R }1$ $177 \div 6 = 29\text{ R }3$ $177 \div 10 = 17\text{ R }7$ $177 \div 12 = 14\text{ R }9$ The only answer choice that divides into $177$ with no remainder is $3$ $ 59$ $3$ $177$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $3$ are contained within the prime factors of $177$ $177 = 3\times59 3 = 3$ Therefore the only factor of $177$ out of our choices is $3$. We can say that $177$ is divisible by $3$.